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Search: id:A077814
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| A077814 |
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#{0<=k<=n: mod(kn,4)=2 }. |
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+0
4
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| 0, 0, 1, 1, 0, 1, 3, 2, 0, 2, 5, 3, 0, 3, 7, 4, 0, 4, 9, 5, 0, 5, 11, 6, 0, 6, 13, 7, 0, 7, 15, 8, 0, 8, 17, 9, 0, 9, 19, 10, 0, 10, 21, 11, 0, 11, 23, 12, 0, 12, 25, 13, 0, 13, 27, 14, 0, 14, 29, 15, 0, 15, 31, 16, 0, 16, 33, 17, 0, 17, 35, 18, 0, 18, 37, 19, 0, 19, 39, 20, 0, 20, 41, 21, 0
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Coefficients in the unique expansion of e/4 = Sum[a(n)/n!, n>=1], where a(n) satisfies 0<=a(n)<n-1.
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FORMULA
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a(n)=0 if n=4k, a(n)=k if n=4k+1, a(n)=2k+1 if n=4k+2 and a(n)=k+1 if n=4k+3.
a(n) = floor(n!*e/4) - n*floor((n-1)!*e/4). - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 07 2002
a(n)=sum{k=0..n, if (mod(nk, 4)=2, 1, 0)}. E.g. a(6)=#{1, 3, 5}=3. - Paul Barry (pbarry(AT)wit.ie), Sep 10 2003
O.g.f.: x^2(1-x+x^2)/((x-1)^2*(1+x^2)^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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EXAMPLE
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sum(i=1,10,a(i)/i!)=0.6795703813... exp(1)/4=0.679570457...
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MATHEMATICA
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a = Table[0, {i, 1, 50}]; x = Exp[1]/4; For[n = 2, n <= 51, n++, { an = 0; While [(x >= (1/n!)) && (an < (n - 1)), {an++, x = x - (1/n!)} ]}; a[[n - 1]] = an; ]; a
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CROSSREFS
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Cf. A009947, A087509, A087620.
Sequence in context: A054503 A122861 A129576 this_sequence A131728 A075115 A085080
Adjacent sequences: A077811 A077812 A077813 this_sequence A077815 A077816 A077817
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Dec 03 2002
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 07 2002
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